Moving the 'center of the object' to the actual center...
Changing the Center is easily done with the moster of a shortcut Ctrl + Shift + Alt + C.From the dropdown select


Origin to geometry If you want to move the center.
Geometry to origin If you want to move the mesh.


If you want finer grade control of the position of the center, you can go to Edit mode by hitting Tab, select all vertices by hitting  A and move the mesh with the widgets. The center doesn't move, so you can position the mesh onto the center like this.

In Object Mode you can center an object so that the center is at the center of the scene (by moving the mesh) with the hotkey Alt + G.

I hope this helps.